fulltext

Factorial correlators from

Au-emulsion collisions at 10.6A GeV (*)

High Energy Experimental Laboratory, Department of Physics State University of New York at Buffalo - Buffalo, NY 14260, USA

(ricevuto il 10 Novembre 1995; revisionato il 10 Febbraio 1997; approvato il 7 Maggio 1997)

Summary. — We compute the factorial correlators, in terms of a new scaled variable X suggested by Bialas and Gazdzicki, to study the dynamical fluctuations of the produced shower particles in different domains of the pseudorapidity phase space. An asymptotic power-law dependence of the factorial correlators, similar to that of scaled factorial moments, has been found in the semi-central interactions of197_{Au at}

10.6A GeV with nuclear emulsion. The consistency of197_{Au results is checked with}

the predictions of a-model for the existence of intermittency. These results are compared with our data for the32_{S and}16_{O beams obtained from the CERN SPS in}

an Experiment No. EMU08.

PACS 25.75 – Relativistic heavy-ion collisions.

1. – Introduction

The most commonly used technique to investigate the origin of nonstatistical fluctuations, occurring in the multiplicity distributions of the secondary particles produced in high-energy collisions, was introduced by Bialas and Peschanski [1]. Their technique seems to be one of the most powerful and promising possibilities for the analysis of event-by-event basis data in terms of intermittency. This technique involves the computation of scaled factorial moments Fi as a function of the decreasing phase-space cells and reveals the self-similar properties of local particle-density fluctuations in multiparticle production at relativistic energy. The power-law behavior of the scaled factorial moments [1] is known as intermittency in analogy with the description of bursts of turbulence in the theory of chaos. The technique of Fimoments has been applied successfully to understand the self-similarity of the hadronization mechanism prevailing in leptonic [2], hadronic [3] and nuclear collisions [4] at relativistic energies. Most of the results on the scaled factorial moments observed by NA35 and WA80 Collaborations [5] have been explained through the Bose-Einstein correlations. In hadronic and nuclear collisions, standard particle production models [6] such as the Lund Monte Carlo Model FRITIOF, are unable to reproduce the experimental results. Therefore, a large number of alternating interpretations, such as

(*) The author of this paper has agreed to not receive the proofs for correction.

conventional short-range correlations and Bose-Einstein interference through the formation of pencil jets, extended parton cascading mechanism of hadrons and a possible signal of quark-gluon plasma, is not ruled out. Since various data sets support different interpretations, more discriminative information is definitely required experi-mentally on this interesting subject using some alternating approach.

Rather than investigating the local particle-density fluctuations through the computation of usual Fi moments as it is done in the case of intermittency, Bialas and Peschanski [1] have also suggested a technique to explore the additional information contained in the local non-statistical fluctuations via the study of factorial correlators (FCs) in different domains of the phase space. In comparison with the scaled factorial moments, very scanty experimental data exist on the study of factorial correlators at high energy. Only two investigations have reported the results on factorial correlators in hadron-hadron [7] and hadron-nucleus collisions [8]. On the other hand, in nucleus-nucleus collisions at CERN energies, the situation is still far from satisfactory: only one emulsion experiment is performed on factorial correlators [9]. As far we know, no data exist on this interesting topic in nucleus-nucleus collisions at the Brookhaven National Laboratory Alternating Gradient Synchrotron (AGS) energy. Therefore, it appears extremely appropriate to analyze the data collected on nucleus-nucleus interactions in an emulsion experiment (No. 875) performed at the AGS using a newly extracted 197_{Au projectile at 10.6A GeV. To achieve our objective, we explore the}

existence of non-statistical fluctuations through the study of factorial correlators in the currently collected data on 197_{Au-emulsion collisions in the pseudorapidity (h) phase}

space with the help of a new scaled variable X suggested by Bialas and Gazdzicki [10]. Furthermore, we compare the results of197Au beam with three additional data samples obtained from the CERN SPS in an Experiment No. EMU08: i) 32_{S ion at}

200A GeV [11], ii)16_{O projectile at 200A GeV [12] and iii)}16_{O beam at 60A GeV [12]. The}

experimental results thus obtained will be confronted with the predictions of

a-model [13]. The results of 197_{Au beam are compared with the simulated data of a}

simple Monte Carlo event generator.

2. – Experimental methodology

In experiment No. 875 conducted at the Brookhaven National Laboratory (BNL), we irradiated the Fuji emulsion pellicles to a beam of 197_{Au ions at 10.6A GeV}

(projectile A). The details of scanning and angular measurement techniques can be found in our earlier publications [14, 15]. For this work, angular measurements were made on a sample of 245197_{Au-emulsion collisions such that the projectile fragments of}

charges 1 GZG17 were survived in an interaction, and also the number of singly charged produced shower particles (Ns) in a collision was always more than 50. This

sample of 245 events involved all sorts of interactions with the emulsion targets, NhF 0.

Here, Nh represents the multiplicity of low-energy target tracks emerged during the

excitation of an emulsion nucleus [12, 15]). The produced shower particles Ns are

predominantly relativistic pions with velocity b 4vOcD0.7. As discussed in ref. [16], uninteresting background shower tracks emerging from pionOgamma conversion to e1_e2 _{pairs were excluded while performing the angular measurements. In a similar}

manner, another source of unwanted background due to double counting of the shower tracks was also avoided. In order to measure angles of the shower tracks, usually one has to perform the measurements at a distance more than 100 –200 mm from the

interaction vertex depending on the nature of a given event in emulsion. At the formation point, the tracks due to an e1_e2_{pair can be easily recognized from the grain}

density, which is initially much larger than the grain density of a singly charged pion or a proton track. The tracks of an electron and a positron (low-mass charged particles) emerged in an e1_e2 _{pair, when followed downstream in nuclear emulsion, scatter}

substantially as compared to the tracks of heavy particles like charged pions. In addition, near the formation point the opening angles of e1_e2_{pairs are very small. In}

emulsion work, an experienced observer can easily detect these pairs among the shower tracks. For the angular measurements, one has to visually examine each and every track produced in a nuclear interaction before the measurements are recoded. In each interaction, pairs such as e1_e2_{were found quite often and they were eliminated}

from the data used in the present study. By using reference primary method [12, 16], we achieved an accuracy of 0.1 mrad in measuring the emission angles (u) of shower particles in the central pseudorapidity region [h 42ln tan (uO2) ]. We compared the results of 197_{Au beam at 10.6A GeV (projectile A) with those of three projectiles}

accelerated from the CERN SPS: i) the 32_{S ion at 200A GeV (projectile B), ii)} 16_O

nucleus at 200A GeV (projectile C) and 16_{O beam at 60A GeV (projectile D). For B, C}

and D beams, the data sets were selected in such a way that a complete breakup of the beam nucleus into singly charged projectile fragments was observed in each event. For projectiles B, C and D, the data sets were composed of 200, 280 and 179 interactions, respectively. To get rid of the edge effects for each data set, mostly the central portion of the pseudorapidity range was used. Further, the analysis was restricted to the pionization region in each case. The selected range of pseudorapidity interval was: Dh41.0–3.7 for projectile A; Dh41.0–6.0 for ions B and C; Dh41.025.5 for projectile D. The average multiplicities of the singly charged produced shower particles aNsb in the investigated Dh 4h2-h1 ranges for the ions A, B, C and D are

129.1 68.2, 195.9613.9, 108.266.5 and 69.465.2, respectively. With these restrictions on pseudorapidity span for each projectile, we are effectively left with i) the analysis of produced singly charged shower particles that are predominently pions. ii) Projectile fragments of charge Z F1 have been excluded by implementing the concept of Fermi momentum cone of angle U 40.2Opbeam, where pbeam is the beam momentum per

nucleon. iii) Target fragments that appear as black Nb and grey Ng tracks in emulsion

are excluded from the present study. In emulsion, the target fragments are mostly low-energy protons (EpE 400 MeV ) or heavier fragments of charge Z F 2 and their

ranges are usually very small. iv) All the e1_e2 _{pairs detected in an interaction were}

excluded as explained earlier.

As discussed above, we performed our analysis almost in the central portions of the singly charged particle pseudorapidity density distribution r for the projectiles A, B, C and D, and hence the creation of a new scaled variable X as suggested by Bialas and Gazdzicki [10] does not change significantly the conclusions of our experiment. The scaled variable X(h) is related to the single-particle density distribution r(h 8) as

X(h) 4



N



where h1and h2 represent two extreme boundaries of the pseudorapidity distribution

for a particular data sample. For an individual produced shower track in a given event, the X-variable was created using eq. (1) corresponding to the pseudorapidity h of that

track falling in the interval Dh 4h22 h1. The variable X varies uniformly between 0.0

to 1.0, so that r(X) B const within h1 and h2as reported in refs. [11, 16]. The present

analysis, therefore, deals with the computation of factorial correlators from the single-particle X(h) distribution rather than the usual pseudorapidity h distribution.

3. – Theoretical formalism

To search for the local-particle density fluctuations in terms of experimental parameters, the scaled factorial moments Fi[1] are computed for N singly charged shower particles falling in a given interval DX 4Xmax2 Xminas follows:

aFib 4 1 M m 41

!

where M is the number of phase-space cells of size dX 4DXOM. nm denotes the multiplicity of produced shower particles detected in the m-th cell and N 4

!

dX for the self-similar fluctuations is expressed as

aFib P (DXOdX)ai, (3)

where the exponents aiare known as the “intermittency exponents”.

To figure out the correlation among the local non-statistical fluctuations occurring in different regions of phase space, we proceed with the computation of factorial correlators from the relation [1]:

aFijmm 8b 4

anm(nm2 1 ) R (nm2 i 1 1 ) 3

(

)

, (4)

where nm and nm 8 are the multiplicities of shower particles in m and m 8 cells, respectively. The factorial correlators are computed at a given value of dX for each combination of mm 8 and then an average is evaluated over all possible combinations with a particular cell separation D between m and m 8 cells.

According to the predictions of a-model [1, 13], intermittency signal in different regions of the phase space should depend on the cell separation D and not on dX, so that the factorial correlators aFijb can be expressed in the form of a power law

aFijb P (DXOD)aij. (5)

When plotted on a log-log scale, the slope parameters aij from eq. (5) and the intermittency exponents from eq. (3) can be correlated [1, 13] as

aij4 ai 1j2 ai2 aj4 ija2,

(6)

where the first equality sign is due to the a-model and the second one is due to the log-normal approximation from the central limit theorem. From eq. (6), it is trivial to

prove that a114 a2and thus we have

aij4 ija2,

(7)

which correlates the factorial correlator slopes aij with the intermittency slope a2 of

order 2.

4. – Results and discussion

In fig. 1(a), (b), (c) and (d), we plot the variation of ln aFijb as a function of 2ln D for projectiles A, B, C and D, respectively, by fixing the value of dX 40.1. Except for the first three data points, for almost every ij order, a linear increase of ln aFijb with 2ln D is observed in each case of fig. 1. Thus, all the ions A, B, C and D obey a power-law behavior given by eq. (5). In the present analysis, we could estimate aFijb up to third order of i and second order of j. The statistical errors, in general, are smaller than the size of a data point and are not plotted in these figures. This is due to the fact that the average multiplicity of produced shower particles at AGS and CERN energies is quite high (NsF 69 ), and hence a large number of combinations can be formed among m and

m8 cells for a given cell separation D. The dotted curves shown in figs. 1(a), 2(a), 3(a)

Fig. 1. – A plot of ln aFi jb as a function of 2ln D with dX40.1 for (a)197Au at 10.6A GeV, (b)32S at

200A GeV, (c) 16_{O at 200A GeV and (d)} 16_{O at 60A GeV. Solid lines in these figures represent}

least-squares fits through a linear portion of the data points. Dotted lines in fig. 1(a) are the results of simulated events for197_{Au data at 10.6A GeV.}

and 4(a) for the 197_{Au beam are due to a randomly generated sample using a simple}

Monte Carlo event generator, which will be discussed later on. In ref. [17], we observed that for the197

Au data at 10.6A GeV the cumulant moments of orders q 42 and 3 are nonzero. However for the CERN projectiles B, C and D [18], all the cumulant moments were zero except of order q 42. Due to these reasons, we present the results of simulated data for the197_{Au projectile only.}

To explore if the power-law behavior is still retained, we reduce the cell size and repeat the above analysis. Once again, we observe a power-law behavior of aFijb as a function of D for these four projectiles. This is shown in figs. 2 and 3 for two cell sizes

dX 40.05 and 0.033, respectively. To examine the fine structure of the factorial

correlators by decreasing the cell size down to dX 40.025, we present the results of projectiles A, B and C in figs. 4(a), 4(b) and 4(c), respectively. The power-law behavior can still be observed in our data, except for a few data points in the beginning. In figs. 2, 3 and 4, the errors were always less than the size of a data point as explained before and hence are not shown. In figs. 2, 3 and 4, we investigated the factorial correlators up to i 43 and j42.

From figs. 1, 2, 3 and 4, the slope parameters aij are obtained by straight line fits through the linear portion of the data points for projectiles A, B, C and D, and are shown by solid lines in these figures. In the least-squares fitting of the data for ions A, B, C and D as shown in figs. 1, 2, 3 and 4, we exclude first 3, 9, 15 and 21 data points,

Fig. 2. – The same as in fig. 1, but for dX40.05. Dotted lines in fig. 2(a) are the results of simulated events for197_{Au data at 10.6A GeV.}

Fig. 3. – The same as in fig. 1, but for the ions A, B and C with dX40.033. Dotted lines in fig. 3(a) are the results of simulated events for197_{Au data at 10.6A GeV.}

Fig. 4. – The same as in fig. 1, but for the ions A, B and C with dX 40.025. Dotted lines in fig. 4a) are the results of simulated events for197_{Au data at 10.6A GeV.}

respectively. This is done in order to avoid the bending that is occurring in the initial parts of all the diagrams. The aijvalues, along with their statistical errors, as obtained from the above fittings are listed in tables I and II for dX 40.1, 0.05, 0.033 and 0.025 for the four ions used. The selected region of D value is chosen in such a way that the maximum of the D-range is almost fixed for different dX values. However, the initial value of the D-range depends upon dX and is different in each case. From tables I and II, we may draw the following inferences: i) The slope values aijare always positive for the investigated ranges of i and j for the projectiles A, B, C and D. ii) For a particular value of dX, a general trend of an enhancement in the aijvalues is observed when the orders i and j are increased for all the data sets. However for projectiles A and B, the slope a22 does not satisfy the above-mentioned condition for four values of dX. This

slope value a22 of the projectile D also does not obey the above condition for dX 40.1

and dX 40.025. iii) By fixing i and j values simultaneously for all the projectiles, a systematic decrease in the slope values aijis noticed as dX is reduced from 0.1 to 0.025. However, for the 32S data at 200A GeV the slope value a32, within statistical errors,

remains unchanged for all values of dX, and the same is true for the 16_{O data at}

60A GeV when dX 40.05 and 0.033. The observations i), ii) and iii) are in qualitative agreement with the findings reported in refs. [7, 8]. From tables I and II, it is obvious

TABLE I. – Values of slopes aij for197Au at 10.6A GeV and32S at 200A GeV projectiles in the

D-ranges as indicated within brackets.

197_{Au at 10.6A GeV} i j dX 40.1 dX 40.05 dX 40.033 dX 40.025 (0.1 GDG0.6) (0.05 GDG0.50) (0.033 GDG0.466) (0.025 GDG0.45) 11 0.0263 60.0017 0.0136 60.0009 0.0103 60.0007 0.0078 60.0005 21 0.0476 60.0030 0.0247 60.0016 0.0166 60.0011 0.0118 60.0008 31 0.0627 60.0040 0.0329 60.0021 0.0203 60.0013 0.0142 60.0009 22 0.0627 60.0040 0.0249 60.0016 0.0180 60.0011 0.0124 60.0008 32 0.0926 60.0059 0.0450 60.0029 0.0301 60.0019 0.0211 60.0013 32_{S at 200A GeV} i j dX 40.1 dX 40.05 dX 40.033 dX 40.025 (0.1 GDG0.6) (0.05 GDG0.50) (0.033 GDG0.466) (0.025 GDG0.45) 11 0.0186 60.0013 0.0161 60.0011 0.0135 60.0010 0.0124 60.0009 21 0.0345 60.0024 0.0316 60.0022 0.0279 60.0020 0.0250 60.0018 31 0.0516 60.0036 0.0514 60.0036 0.0497 60.0035 0.0439 60.0031 22 0.0471 60.0033 0.0429 60.0028 0.0377 60.0027 0.0329 60.0023 32 0.0685 60.0048 0.0688 60.0049 0.0690 60.0049 0.0619 60.0044

that the maximum value of D-range is almost constant for all the ions used in this experiment. But the minimum D-range is entirely different for the four projectiles as it depends upon a given value of dX. Therefore, it natural to think that the slope of the ln aFijb vs. 2ln dD plot should depend upon the selected range of D and this is what is observed from tables I and II. Similar results are also reported in refs. [7, 8].

We now investigate the variation of ln aFijb as a function of 2ln dX by fixing the value of D 40.025, and this is shown in fig. 5(a), 5(b) and 5(c) for197_{Au at 10.6A GeV,}32_S

at 200A GeV and 16_{O at 200A GeV, respectively. As expected from the predictions of}

a-model, figs. 5(a), 5(b) and 5(c) reveal a common feature of aFijb that does not depend on the cell size dX. However, the results of 16_{O at 60A GeV were contrary to the}

predictions of a-model (and are not shown in fig. 5).

Using eq. (7), a connection between the factorial correlators aFijb and factorial moments aFib can be established. Thus, we computed the factorial moments for projectiles A, B, C and D using the X-variable exactly in the same Dh-range for each beam as was done in this experiment. The a2 values as determined from the

least-squares fitting of the data points for the projectiles A, B, C and D in their respective orders are: a24 0.006 6 0.001, 0.009 6 0.001, 0.014 6 0.001 and 0.008 6 0.001.

By inserting the above values of a2, one can obtain the corresponding aFijb values and the prediction (7) of the a-model can be tested for different ranges of D given in tables I and II for the projectiles A, B, C and D. For all the beams, the calculated aFijb values from the given a2 values do not match with their corresponding values for any of the

D-range . Therefore, the prediction represented by eq. (7) is found to be invalid for all

TABLEII. – Same as in table I, but for16_{O at 200A GeV and 60A GeV.} 16_{O at 200A GeV} i j dX 40.1 dX 40.05 dX 40.033 dX 40.025 (0.1 GDG0.6) (0.05 GDG0.50) (0.033 GDG0.466) (0.025GDG0.45) 11 0.0355 60.0021 0.0216 60.0013 0.0183 60.0011 0.0154 60.0009 21 0.0630 60.0038 0.0457 60.0027 0.0358 60.0021 0.0327 60.0020 31 0.0852 60.0051 0.0668 60.0040 0.0545 60.0033 0.0476 60.0033 22 0.0982 60.0059 0.0774 60.0046 0.0587 60.0035 0.0517 60.0031 32 0.1391 60.0083 0.1192 60.0071 0.0923 60.0055 0.0775 60.0046 16_{O at 60A GeV} i j dX 40.1 dX 40.05 dX 40.033 dX 40.025 (0.1 GDG0.6) (0.05 GDG0.50) (0.033 GDG0.466) (0.025 GDG0.45) 11 0.0264 60.0020 0.0166 60.0012 0.0102 60.0008 0.0082 60.0006 21 0.0456 60.0034 0.0312 60.0023 0.0229 60.0017 0.0172 60.0013 31 0.0651 60.0049 0.0398 60.0030 0.0311 60.0023 0.0261 60.0020 22 0.0652 60.0049 0.0472 60.0035 0.0351 60.0026 0.0103 60.0007 32 0.0992 60.0075 0.0618 60.0046 0.0618 60.0046 0.0272 60.0020

In general, our results are in agreement with the predictions of a-model, and we observe a power law behaviour of the factorial correlators for all the data sets used in this experiment. However, the power-law behaviour may not be considered as a sufficient proof for the existence of non-statistical fluctuations as suggested in ref. [5]. It may be due to some trivial statistical effect. To explore this, we used a simple Monte Carlo event generator that generated the pseudorapidity values corresponding to the multiplicity of shower particles for each event of a given data set. On the generated events, the analysis of factorial correlators was repeated as discussed before. The results of the simulated events are presented in figs. 1(a), 2(a), 3(a) and 4(a) by dotted lines for the197

Au data. For dX 40.1 and 0.05, the variations of ln aFijb as a function of 2ln D are partially similar to the experimental observations for all values of ij, except for the curve with i j 431, where it slightly disagrees with the simulations. Thus, we find that a simple Monte Carlo event genearator may not completely explain the197Au results. Results of the simulated events were also obtained for the CERN beams B, C and D and are not presented in figs. 1, 2, 3 and 4, since our experimental observations were along the lines with those obtained for the simulated data. To examine whether the nonstatistical fluctuations survive for the197

Au data, we reduce the bin size to dX 4 0.033 and 0.025 and present the results in figs. 3(a) and 4(a) with dotted curves. We find that the factorial correlators of higher orders with ij 432 may not be fully explained by the simulated events. This may be a signature of some real dynamics involved in

197_{Au-emulsion collisions at 10.6A GeV. Recently, Carruthers et al. [19] have pointed}

out that the intermittency phenomenon could be understood in terms of conventional short-range correlations among the produced particles, and cumulant moments of higher order than q 42 are strongly suppressed. On the contrary, in a recent investigation on the197_{Au data, we do find that the cumulant moments order q 43 are}

Fig. 5. – A plot of ln aFijb as a function of 2ln dX for: (a)197Au at 10.6A GeV, (b)32S at 200A GeV

and (c)16_{O at 200A GeV.}

nonzero [17] among the shower particles, indicating that there may be some kind of collective phenomenon present among the particles produced in 197_Au-emulsion

interactions [20]. However, our observations of the projectiles B, C and D accelerated at the CERN SPS are consistent with zero values of cumulant moments, except for order q 42 [18]. In another study [21], we find that two- and three-particle correlations (R2and R3) for the central events of197Au at 10.6A GeV are much stronger than those

for the 32_{S data at 200A GeV. Thus, the data of} 197_{Au beam at 10.6A GeV behave}

differently from the data of16_{O projectiles at 60A GeV and 200A GeV as well as of}32_S

beam at 200A GeV.

5. – Conclusions

The analysis of factorial correlators aFijb [1] has been performed in h phase space by using a new scaled variable X(h) suggested by Bialas and Gazdzicki [10]. There are some indications of nonstatistical fluctuations revealed in some regions of phase space in the multiplicity distribution of shower particles produced in197_{Au-emulsion collisions}

at AGS energy. But the significance of these deviations is rather weak and is indicated only by few correlators. The results of the197_{Au beam are compared with the available}

data on 32S at 200A GeV, 16O at 200A GeV and16O at 60A GeV projectiles accelerated from the CERN SPS. The factorial correlators aFijb are observed to increase with decreasing correlation length D for all the projectiles, and they are found to be independent of dX, for beams of197_{Au at 10.6A GeV,} 32_{S at 200A GeV and} 16_{O at 200A}

GeV. These results are qualitatively in agreement with the predictions of a-model [13], and are almost identical to those obtained in hadron-hadron [7], hadron-nucleus [8] and nucleus-nucleus collisions [9]. The log-normal approximation represented by eq. (7) seems to be invalid for the factorial correlators data (tables I and II), when the factorial correlators are computed by using the intermittency slope a2of order 2 for a given data

set. Similar observations are also reported in refs. [7, 8]. A simple Monte Carlo event generator may not completely explain the 197Au-emulsion results on factorial correla-tors. There may be some real dynamical mechanism present such as collectivity, etc., in

197

Au-emulsion data [20], which is further revealed through our recent study of nonzero cumulant moments of order q 43 for the197_{Au data [17].}

* * *

We thankful to the BNL and SPS technical staff for their help in the exposure and to Prof. G. ROMANO for the development of emulsion stacks. This research work was supported by the Department of Energy through Grant No. DE-FG02-90ER40566 and partially by the Research Foundation of SUNY at Buffalo.

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